How do I submit a timesheet for internal approval?

In order to submit timesheet entries for approval process, you will have to first enable internal approval from Settings.

Go to the Time Tracking module and click Approvals tab.
Click + New Approval button.
Choose the project for which you want to submit time entries for approval from the Projects field.
Enter an Approval Name and a Description for the approval.
Under Timesheet, choose the respective time entries which you wish to submit for approval.
Click Save and Submit.